Subharmonicity in von Neumann algebras

Let M be a von Neumann algebra with unit 1(M). Let tau be a faithful, normal, semifinite trace on M. Given x epsilon M, denote by mu(t)(x)t >= o the generalized s-numbers of x, defined by mu(t)(x) = inf{parallel to xe parallel to : e is a projection in M with tau(1(M) - e) <= t} (t >= 0). We prove that, if D is a complex domain and f : D -> M is a holomorphic function, then, for each t >= 0, lambda -> integral(0)(t) log mu(s) (f (lambda)) ds is a subharmonic function on D. This generalizes earlier subharmonicity results of White and Aupetit on the singular values of matrices.